chapter twelve 12-1. census: population canvass - not really a “sample” asking the entire...

Chapter Twelve

12-1

Census:• Population canvass - not really a “sample”• Asking the entire population

Budget Available:• A valid factor – how much can we afford?

Rule of Thumb:• Is there some convention we can apply?• What might make an adequate sample size?

Sample Size for Probability Sampling

12-2Key Terms & Definitions

Number of Subgroups Analyzed:In any sample size determination problem, consideration must be given to the number and anticipated size of various subgroups of the total sample that must be analyzed.

Traditional Statistical Methods:Variance, standard deviation, and confidence interval play a key role.

Sample Size for Probability Sampling


Judgment:• Best guess of “experts”• Draw on your experience to determine sample

size

Conventional:• What have others done?• See what the sample size has been for similar

studies

Sample Size for Nonprobability Sampling


Central Limit Theorem:

The idea that a distribution of a large number of sample means or sample proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn.

Normal Distribution:

The continuous distribution that is bell shaped and symmetrical about the mean. The mean, median, and mode are equal. Finally, about 68% of the observations are within one standard deviation plus/minus of the mean, 96% are within two standard deviations, and 99+% are within three standard deviations of the mean respectively.

The Normal Distribution


Proportionate Properties of the Normal Distribution: A feature that the number of observations falling between the mean and a given number of standard deviations from the mean is the same for all normal distributions.



Standard Normal Distribution: Normal distribution with a mean of zero and a standard deviation of one.



Standard Deviation:

The measure of dispersion calculated by subtracting the mean of the series from each value in a series, squaring each result, summing the results, dividing the sum by the number of observations minus 1 and finally taking the square root of this value.

StandardDeviation

(N-1)

(X - X)12

= sumStandard

Deviation(N-1)

(X - X)12

= sum



Important Characteristics of a Normal Distribution


1. Bell-shaped and has only one mode.

2. Symmetric about its mean.

3. Uniquely defined by its mean and standard deviation.

4. The total area under a normal curve is equal to one.

5. The area of a region under the normal distribution curve between any two values of a variable equals the probability of observing a value in that range when an observation is randomly selected from the distribution.

6. The area between the mean and a given number of standard deviations from the mean is the same for all normal distributions.

Population Distribution: The frequency distribution of all the elements of a population.

Sampling Distribution:

The frequency distribution of all the elements of an individual sample.

Population and Sampling Distribution


Sampling Distribution of the Mean:

The theoretical frequency distribution of the means of all possible samples of a given size drawn from a particular population; it is normally distributed.

Sampling Distribution of the Mean


Standard Error of the Mean:

Standard deviation of a distribution of sample means.

Standard Error of the Mean


Relationships of the Three Basic Types of Distribution


Simple Random Sample


The results of a simple random sample of fast-food restaurant patrons could be used to compute the mean number of visits for the period of 1 month for 1,000 samples.

Simple Random Sample


Point Estimate:

The particular estimate of a population value.

Interval Estimate:

The interval or range of values within which the true population value is estimated to fall.

Point and Interval Estimations


Confidence Level:

The probability that a particular interval will include the true population value; also called the confidence coefficient.

Confidence Interval:

The interval that, at the specified confidence level, includes the true population value.

Confidence Level and Interval


Sampling Distribution of the Proportion:

The relative frequency distribution of the sample proportions of many random samples of a given size drawn from a particular population; it is normally distributed.

Sampling Distribution of the Proportion


Examples:

• The percentage of a population is aware of a particular ad.

• The percentage of the population that accesses the Internet one or more times in an average week.

• The percentage of the population that has visited a fast-food restaurant four or more times in the past 30 days.

• The percentage of the population that watches a particular television program.

Sampling Distribution of the Proportion


Problems Involving Mean:

Determining the Sampling Size



1. Allowable Sampling Error:

Amount of sampling error the researcher is willing to accept, E.

2. The Acceptable Level of Confidence:

How confident does the researcher want to be that an interval includes the population mean, Z.

3. Population Standard Deviation:

Standard deviation of a variable for the entire population, σ.



Determining Population Standard Deviation:

How to determine before selecting the sample:

• Use results from a prior surveyo In many cases, your firm may have conducted a prior survey

dealing with similar subject matter.• Conduct a pilot survey

o For a large-scale project, you may conduct a smaller-scale pilot to help determine your standard deviation.

• Use secondary datao Using secondary resources to accumulate data about your

population sample.• Use judgment

o When all else fails, estimating it based on your educated judgment.


Problems Involving Proportions:



Population Size and Sampling Size

Independence Assumption:

Assumption that sample elements are drawn independently.


ErrorsStatistical Errors:

Most of the formulas in this unit focus on determining type I errors or the error that concludes there is a difference when there is no actual difference.

A type II error is one where you say there is no difference when there is an actual difference. The probability of not making this type of error is called statistical power.


Finite Population Correction Factor (FPC)Statistical Power:

The probability of not making a type II error.


Determining the number of phone numbers you’ll need to connect with the sample size you desire requires:

• The number of completed interviews you need.

• The working phone or “reachable” rate.

• The incidence rate or the number of the people you call who will answer and qualify for the interview.

• The contact/completion rate which includes:o Contact rateo Length of interviewo Sensitivity of topico Time of yearo Number of callbacks

How Many Contacts?


You need to contact more than n, since it’s unlikely that everyone you contact will agree to answer the questionnaire. If you determine that you need 800 respondents and a typical response rate for your type of survey is 30%, then you would actually have to contact 2,667 people to get 800 completed surveys.

How Many Contacts?


Number of Contacts = n/.30OR

800/.3Number of Contacts = 2,667

You must contact approximately 2,667 people (with 30% response rate), so you can expect 800 people to

respond (the final sample size).

• Time to Generate the Sample• Scope of the Research• Budget Available• Experience with Sampling• Level of Accuracy Desired• Your Knowledge of the Population

Sampling Issues To Consider

12-29

12-30

Key Terms & Definitions

• Central Limit Theorem• Normal Distribution• Proportional Property of the Normal

Distribution• Standard Normal Distribution• Sample Size for Nonprobability Sampling• Standard Deviation• Population Distribution• Sample Distribution• Sampling Distribution of the Mean

Links and button are active when in “Slide Show Mode”Key Terms & Definitions

• Standard Error of the Mean• Point Estimate• Interval Estimate• Confidence Level• Confidence Interval• Sampling Distribution of the Proportion• Allowable Sampling Error• Population Standard Deviation• Finite Population Correction Factor (FPC)• Statistical Power

chapter twelve 12-1. census: population canvass - not really a “sample” asking the entire...

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